Multivariate Nonlinear Causality Testing

In this thesis, we give a brief review on the theory of linear Granger causality, intro-ducing two testing methods for the vector autoregression model (VAR) and ECM-VAR model. We also introduce the simple costationary sequence. Based on that, we extend the method came up with by Hiemstra and Jones (1994) to the multivariate case and propose a multivariate non-linear Granger causality testing method. Furthermore, con-sidering the non-stationarity characteristic of most time series, we extend the method to the special non-stationary co-integrated models.we conduct the Monte Carlo simulations and compare our method with bivari-ate testing method. We assign different values to β, sample size and lag length and analyze the outcoming data. Through data stimulation and analysis of the graphs we can say with confidence that our method clearly performs better than bivariate testing method.finally, we investigate different values of the parameter and come to the conclusion that picking the parameter e reasonally has a great influence on the effectiveness of the method.